How this calculator works
A periodic function assigns the same ratio to many angles. An inverse therefore needs a restricted branch to return one angle. Arcsine and arccosine accept ratios from -1 to 1, while arctangent accepts every finite ratio. Reciprocal inverse functions apply arcsine or arccosine to 1/x; arccotangent uses angles strictly between 0° and 180°. The reverse mode accepts only the selected principal branch.
Formula
sin(arcsin x)=x, cos(arccos x)=x, tan(arctan x)=x. arcsec x=arccos(1/x); arccsc x=arcsin(1/x); arccot x=atan2(1,x).
Worked example
arcsin(0.5) = 30° = π/6 radians. arccos(-1) = 180°. arctan(1) = 45°. Under the stated arccotangent convention, arccot(-1) = 135°.
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Frequently asked questions
Does sin⁻¹ mean one divided by sine?
In inverse-function notation it means arcsine. The reciprocal 1/sin x is cosecant, a different function.
Why is arcsin(sin 150°) only 30°?
Both angles have sine 0.5, but arcsine returns the value within its principal range from -90° to 90°.
Are there other arccotangent conventions?
Yes. This tool uses (0°, 180°). Check the convention expected by your course when working with negative arguments.